Quantum Grover Attack on the Simplified-AES

In this work, a quantum design for the Simplified-Advanced Encryption Standard (S-AES) algorithm is presented. Also, a quantum Grover attack is modeled on the proposed quantum S-AES. First, quantum circuits for the main components of S-AES in the finite field F2[x]/(x4 + x + 1), are constructed. Then, the constructed circuits are put together to form a quantum version of S-AES. A C-NOT synthesis is used to decompose some of the functions to reduce the number of the needed qubits. The quantum S-AES is integrated into a black-box queried by Grover's algorithm. A new approach is proposed to uniquely recover the secret key when Grover attack is applied. The entire work is simulated and tested on a quantum mechanics simulator. The complexity analysis shows that a block cipher can be designed as a quantum circuit with a polynomial cost. In addition, the secret key is recovered in quadratic speedup as promised by Grover's algorithm.

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